Multiple blowing-up solutions for asymptotically critical Lane-Emden systems on Riemannian manifolds (Q6604715)

Using the Lyapunov-Schmidt reduction method, the authors prove the existence of multiple blow-up solutions for the elliptic problem\N\begin{gather*}\N-\Delta_gu+h(x)u=v^{p-\alpha \epsilon},\\\N-\Delta_gv+h(x)v=v^{q-\beta \epsilon}\N\end{gather*}\Nfor the positive \(u\), \(v\) on a smooth compact Riemannian manifold~\((\mathcal M,g)\) of dimension~\(N\geqslant8\). Here, \(\Delta_g\) is the Laplace-Beltrami operator on~\(\mathcal M\), \(h(x)\) is a \(C^1\)-function on~\(\mathcal M\), \(\epsilon\) is a small parameter, \(\alpha,\beta>0\) and \(p\) and \(q\) satisfy \(\frac1{p+1}+\frac1{q+1}=\frac{N-2}N\), \(p>1\), \(q>1\).